The principal value of \(\cos^{-1}\left(-\displaystyle\frac{1}{2}\right)\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{2\pi}{3}\)
The principal value branch of \(\cos^{-1}\) is \([0, \pi]\). Using \(\cos^{-1}(-x) = \pi - \cos^{-1}x\):
\( \displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \pi - \cos^{-1}\frac{1}{2} \)
\( \displaystyle = \pi - \frac{\pi}{3} = \frac{2\pi}{3} \)
Check: \(\cos\frac{2\pi}{3} = -\frac{1}{2}\) and \(\frac{2\pi}{3}\) lies in \([0, \pi]\).
NCERT (2026-27 edition):
Basic Concepts
